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The AND and NOT gates are called the complete set as any logic function can be represented by specifically connecting certain number of these two gates. Figure 2.17 shows the structure of ANDANDNOT logic gate which is preferable to a cascaded two-enzyme circuit. A single enzyme can implement this logic gate. The ANDANDNOT gate can be formed by combining two activating stem-loop regions to one inhibitory stem-loop region. The gate gets activated by the addition of two input oligonucleotides, ix and iy. But the presence of another input signal ix inhibits the substrate to anneal to its binding region. This logic gate as represented in Figure 2.17 computes xAND yAND NOTz. Table 2.6 represents the truth table for ANDANDNOT gate.

But deoxyribozyme logic gates have certain drawbacks in performing logical operations for large DNA logic circuits. The mechanism explained above takes small sequences as input and produces cleaved or ligated oligonucleotide as the output signal which has different formation than input signal. Thus, the cascading operations become complicated. But, to develop and control nano-scale devices, designing large DNA logic circuit is crucial. This problem has been solved by Seelig and co-workers [8] who have implemented enzymefree logic circuits by nucleic acids.

Figure 2.17 Structure of ANDANDNOT gate.

Table 2.6 Truth table for ANDANDNOT gate.

Input (ix)	Input (iy)	Input (iz)	Output
0	0	0	0
1	0	0	0
0	1	0	0
1	1	0	1
0	0	1	0
1	0	1	0
0	1	1	0
1	1	1	0